It depends on the type of contract, but usually the wet ink signing must usually take place at a given date in a given place. However more often than not you can give a power of attorney to the lawyers representing you and they usually sign together.
However, a contract is only valid and enforceable if both parties have signed it (and if no clauses are illegal of course).
So if De Gea signed it on his side, but the club hasn’t yet, technically the renewal isn’t effective yet and the club can change its mind about this or that clause.
It’s not a common situation though as it’s bad for business relationships (you’re only as good as your word) but nothing illegal the way I ser it
I can't speak to the procedural requirements of contract law in the UK, but as a general practice digital signatures are now commonly accepted as binding in the US and I see no reason why that wouldn't be the case in the UK as well. Under general principles of contract law, if an offer is made and accepted a contract is entered into. It would be highly irregular for an offer in good faith to be made without a signature of the party making the offer on the document itself that only requires a signature of the accepting party to sign. If in fact an actual contract offer was by Manchester United Football Club it had to have been an offer in writing and affixed with a signature by the officer (a US term, probably not the UK term) of the organization -- in this case, a football club -- with the legal authority to sign player contracts.
If on the other hand, a document that represents a good faith offer by the club was presented to the player that did not have the signature of the officer the organization right off the bat that is completely out of order and De Gea had every right to sat WTF is this shite? (De Gea critics could well respond WTF was the Benrhama goal or the second Gundogan goal all about?) The organization would do this -- that is, withhold from affixing a signature to the contract it offered -- only if it had always planned on withdrawing the offer to the player in the event he actually signed it. Which would be a disgraceful play by the club. In this case what I'm reading online is that De Gea accepted the offer with his signature but that after he affixed signature to the contract that the club immediately withdrew its offer that it never signed when it made the offer. An appalling and disgraceful treatment of the player, whatever one thinks of his performances over the last month or the last decade.
Re the other points re a given date and a given place, a contract may include such stipulations -- that the offer is only an offer until X date and that if it is to be a binding contract it must be signed at a specific location such as Old Trafford, but as a general principle of contract law a contract can be binding if the contract itself is signed by both parties at their leisure.